nb/2022-01-04__Hello_Julia.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2022-01-04 • Hello Julia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time to evaluate this code cell after kernel restart: 14 à 21 seconds.  \n",
    "So restarting kernel is to be avoided..\n",
    "\n",
    "Also note, starting julia interpreter in terminal is faster, less than a second."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  9.133000 seconds (8.27 M allocations: 572.587 MiB, 2.80% gc time, 8.71% compilation time)\n"
     ]
    }
   ],
   "source": [
    "@time using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Plots.GRBackend()"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "default(legend=:none, size=(300,120))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "Random.seed!(2022)\n",
    "\n",
    "x = randn(10);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.000854 seconds (1.29 k allocations: 74.836 KiB)\n"
     ]
    },
    {
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     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time plot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.000031 seconds (6 allocations: 576 bytes)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Plots.PyPlotBackend()"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time pyplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can set default with `ENV[\"PLOTS_DEFAULT_BACKEND\"] = \"pyplot\"`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "import PyPlot: matplotlib, subplots, version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 400x300 with 4 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.lines.Line2D object at 0x0000000096C6FD00>"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = subplots(2,2, figsize=(4,3))\n",
    "fig.suptitle(\"Hello ♥ Matplotlib\")\n",
    "fig.tight_layout()\n",
    "ax[1,1].stairs(x)\n",
    "ax[1,2].stem(x)\n",
    "ax[2,2].axhline(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.transforms.Affine2D object at 0x0000000084780520>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig.dpi_scale_trans"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Amazing. We have access to the _entirety_ of matplotlib (and an up-to-date version too)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mpl version 3.5.1"
     ]
    }
   ],
   "source": [
    "print(\"mpl version $version\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Units "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.397959 seconds (710.74 k allocations: 45.410 MiB, 0.77% compilation time)\n"
     ]
    }
   ],
   "source": [
    "@time using Unitful, UnitfulRecipes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Unitful.DefaultSymbols  # m, cm, …"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ENV[\"UNITFUL_FANCY_EXPONENTS\"] = true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7 cm s⁻¹"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 7cm/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Quantity{Int64, 𝐋 𝐓⁻¹, Unitful.FreeUnits{(cm, s⁻¹), 𝐋 𝐓⁻¹, nothing}}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Quantity{Float64, 𝐋, Unitful.FreeUnits{(m,), 𝐋, nothing}}}:\n",
       "    1.0 m\n",
       "   0.02 m\n",
       " 3000.0 m"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1.0m, 2.0*cm, 3.0 * km]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Vector{Quantity{Int64, 𝐌, Unitful.FreeUnits{(kg,), 𝐌, nothing}}}:\n",
       " 2 kg\n",
       " 3 kg\n",
       " 4 kg\n",
       " 5 kg"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[2:5;] * kg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numeric processing performance of unitful arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [],
   "source": [
    "using BenchmarkTools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [],
   "source": [
    "z, q = randn(2000); randn(2000);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [],
   "source": [
    "zz, qq = z*kg, q*mV/s;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 10000 samples with 9 evaluations.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m1.844 μs\u001b[22m\u001b[39m … \u001b[35m253.278 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m 0.00% … 95.76%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m3.267 μs               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m 0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m4.136 μs\u001b[22m\u001b[39m ± \u001b[32m 11.771 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m15.04% ±  5.24%\n",
       "\n",
       "  \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▂\u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[39m▃\u001b[39m \u001b[34m \u001b[39m\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
       "  \u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▄\u001b[39m█\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[34m▆\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▅\u001b[39m▅\u001b[39m▆\u001b[32m█\u001b[39m\u001b[39m▇\u001b[39m▅\u001b[39m▄\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m▂\n",
       "  1.84 μs\u001b[90m         Histogram: frequency by time\u001b[39m        9.41 μs \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m15.81 KiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m3\u001b[39m."
      ]
     },
     "execution_count": 277,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark zz ./ qq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 10000 samples with 9 evaluations.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m2.744 μs\u001b[22m\u001b[39m … \u001b[35m794.422 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m 0.00% … 98.60%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m4.289 μs               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m 0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m5.606 μs\u001b[22m\u001b[39m ± \u001b[32m 17.058 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m14.77% ±  5.25%\n",
       "\n",
       "  \u001b[39m▆\u001b[39m▂\u001b[39m \u001b[39m▇\u001b[39m \u001b[39m \u001b[39m▃\u001b[39m█\u001b[34m▂\u001b[39m\u001b[39m▃\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
       "  \u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m█\u001b[39m▅\u001b[39m▆\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▄\u001b[39m▃\u001b[32m▃\u001b[39m\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▂\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m▂\n",
       "  2.74 μs\u001b[90m         Histogram: frequency by time\u001b[39m        14.6 μs \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m15.81 KiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m3\u001b[39m."
      ]
     },
     "execution_count": 278,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark z ./ q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unitful array math just as fast as plain float array math 🤯  \n",
    "Thanks to it doing the unit calculations at compile time. Gives verbose types, but fast speedy numerics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Array wrapper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Unitful\n",
    "import Unitful: kg, s, ms, mV, Hz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: replacing module Shorthands.\n"
     ]
    }
   ],
   "source": [
    "module Shorthands\n",
    "const Float = Float64\n",
    "const Optional{T} = Union{T,Nothing} where T\n",
    "const mime_multiline = MIME(\"text/plain\")\n",
    "export Float, Optional, mime_multiline\n",
    "end\n",
    "using .Shorthands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"Add `IOContext` settings to an `IO` object if they have not been set yet.\"\"\"\n",
    "function add_defaults(io::IO, defaults::Pair...)::IO\n",
    "    settings = merge(Dict(defaults), IOContext(io).dict)\n",
    "    IOContext(io, settings...)\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Base.show(io::IO, x::Float) = \n",
    "    Base.@invoke show(add_defaults(io, :compact=>true)::IO, x::Union{Float16,Float32,Float64})\n",
    "    # this works (i.e. is non-recursive) because we only define it for Float64, not the Union"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Base.show(io::IO, ::MIME\"text/plain\", x::Quantity) =\n",
    "    Base.@invoke show(add_defaults(io, :fancy_exponent=>true)::IO, x::Quantity)\n",
    "    # this works because Unitful defined a `show` for both with and without mime; we invoke the without here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3 mV ms⁻¹"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.1*3 * mV/ms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [],
   "source": [
    "#=\n",
    "`showarg` is called by `summary`, which is in turn called by `show`.\n",
    "It is the \"Vector{ElType}\" part in \"300-element Vector{Eltype}: …\"\n",
    "=#\n",
    "\"\"\"Show summary of the type of a unitful array.\"\"\"\n",
    "function Base.showarg(io::IO, x::AbstractArray{<:Quantity}, toplevel)\n",
    "    print(io, x isa Vector ? \"Vector\" : \n",
    "              x isa Matrix ? \"Matrix\" :\n",
    "              nameof(typeof(x)))\n",
    "    el = first(x)\n",
    "    io = add_defaults(io, :fancy_exponent=>true)  # m² instead of m^2\n",
    "    print(io, \"{\", typeof(el.val), \", \", unit(el), \"}\")\n",
    "    # if integrating in Unitful, a todo: handle heterogeneous arrays.\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [],
   "source": [
    "function Base.show(io::IO, ::MIME\"text/plain\", x::AbstractArray{<:Quantity})\n",
    "    summary(io, x)\n",
    "    println(io, \":\")\n",
    "    Base.print_array(io, ustrip(x))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Vector{Int8, kg s⁻¹}:\n",
       "   20\n",
       "  -39\n",
       " -115\n",
       "   91"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand(Int8, 4)kg/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use ctrl-enter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: replacing module S.\n"
     ]
    }
   ],
   "source": [
    "module S\n",
    "\n",
    "import Unitful: Time, Quantity, unit, ustrip, numtype\n",
    "using Base.Iterators\n",
    "using PyFormattedStrings\n",
    "using ..Shorthands\n",
    "using .Main\n",
    "\n",
    "\"\"\"An array where one dimension represents evenly spaced samples in time.\"\"\"\n",
    "struct Signal{T,N} <: AbstractArray{T,N}\n",
    "    \n",
    "    data::AbstractArray{T,N}\n",
    "    \n",
    "    \"\"\"Time between two samples. Reciprocal of sampling frequency.\"\"\"\n",
    "    Δt::Time\n",
    "    \n",
    "    \"\"\"Optional description of the values in `data`. E.g. \"Membrane potential\".\"\"\"\n",
    "    description::Optional{AbstractString}\n",
    "    \n",
    "    \"\"\"Time dimension of the array. Defaults to `1`.\"\"\"\n",
    "    tdim::Int\n",
    "end\n",
    "\n",
    "# Allow `description` and `tdim` as optional keywords.\n",
    "# non-todo: macro this (`Base.@kwdef` or Parameters.jl no good: can't have mix of kw and non-kw).\n",
    "Signal(d, Δt, description; tdim=1) = Signal(d, Δt, description, tdim)\n",
    "Signal(d, Δt; description=nothing, tdim=1) = Signal(d, Δt, description, tdim)\n",
    "\n",
    "Base.size(x::Signal) = size(x.data)\n",
    "Base.getindex(x::Signal{T,N}, I::Vararg{Int, N}) where {T,N} = x.data[I...]\n",
    "Base.setindex!(x::Signal{T,N}, v, I::Vararg{Int, N}) where {T,N} = (x.data[I...] = v)\n",
    "\n",
    "duration(x::Signal) = size(x, x.tdim) * x.Δt\n",
    "\n",
    "function Base.summary(io::IO, x::Signal)\n",
    "    print(io, Base.dims2string(size(x)), ' ')\n",
    "    isnothing(x.description) || print(io, '\"', x.description, '\"', ' ')\n",
    "    Base.showarg(io, x, true)\n",
    "    print(io, \", duration \", duration(x))\n",
    "end\n",
    "\n",
    "function Base.show(io::IO, ::MIME\"text/plain\", x::Signal)\n",
    "    print(io, Base.dims2string(size(x)))\n",
    "    isnothing(x.description) || print(io, ' ', '\"', x.description, '\"')\n",
    "    println(io, \" Signal:\\n\")\n",
    "    el = first(x)\n",
    "    isunitful = (el isa Quantity)\n",
    "    isunitful && (io = Main.add_defaults(io, :fancy_exponent=>true))  # m² instead of m^2\n",
    "    Base.print_array(io, isunitful ? ustrip(x) : x)\n",
    "    println(io, \"\\n\")\n",
    "    printrow(key, val) = println(io, lpad(key, 9), \": \", val)\n",
    "    isunitful && printrow(\"units\", unit(el))\n",
    "    printrow(\"duration\", f\"{duration(x)} (Δt: {x.Δt})\")\n",
    "    printrow(\"dtype\", isunitful ? typeof(el.val) : typeof(el))\n",
    "end\n",
    "\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use ctrl-enter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-element \"Membrane potential\" Signal:\n",
       "\n",
       " -0.53508\n",
       " -1.05966\n",
       "  0.200328\n",
       " -2.70706\n",
       " -0.538937\n",
       " -0.63484\n",
       "  0.507051\n",
       "  0.627075\n",
       " -0.663051\n",
       "  0.662328\n",
       " -1.96189\n",
       "  0.441242\n",
       "  0.408328\n",
       "  ⋮\n",
       " -0.222719\n",
       " -0.934877\n",
       "  0.431609\n",
       "  0.0725057\n",
       " -1.36245\n",
       "  2.13669\n",
       "  1.75368\n",
       "  1.04932\n",
       " -0.999424\n",
       "  0.154111\n",
       " -1.05527\n",
       " -0.999598\n",
       "\n",
       "    units: mV ms⁻¹\n",
       " duration: 200.0 ms (Δt: 0.1 ms)\n",
       "    dtype: Float64\n"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = S.Signal(randn(2000)*mV/ms, 0.1*ms, \"Membrane potential\")\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2000-element \"Membrane potential\" Signal(Float64, mV ms⁻¹), duration 200.0 ms"
     ]
    }
   ],
   "source": [
    "print(summary(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×90 Signal:\n",
       "\n",
       "  0.119297   0.109232  -0.380801  …  -0.350973   1.73712   -0.798376\n",
       " -0.307181  -0.422936   0.912106      0.975326  -1.27965    1.26854\n",
       " -0.502739   1.14168    0.899721     -0.52512    0.583211   1.34904\n",
       "\n",
       " duration: 45.0 ms (Δt: 0.5 ms)\n",
       "    dtype: Float64\n"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = S.Signal(randn(3,90), 0.5ms, tdim=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Main.S.Signal{Float64, 2}"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Main.S.Signal{Quantity{Float64, 𝐋^2 𝐌 𝐈^-1 𝐓^-4, Unitful.FreeUnits{(ms^-1, mV), 𝐋^2 𝐌 𝐈^-1 𝐓^-4, nothing}}, 1}"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Unitful: Voltage, Time, Current"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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    {
     "data": {
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       "Union{Quantity{T, 𝐓, U}, Level{L, S, Quantity{T, 𝐓, U}} where {L, S}} where {T, U}"
      ]
     },
     "execution_count": 20,
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     "output_type": "execute_result"
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    "Time"
   ]
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